I'd say multiplexing generally was initially done to save on logic
and hardware. One 1-of-10 decoder instead of 12 or 16 of them, and 10
+12 drivers instead of 120, for example.
Be warned that for some displays the 'electrical' matrix may not
correspond to the physical one.
For example, the LED display in the HP9830 calcualtor is a 7 row by 160
column dot matrix unit (32 chracters, 5 dot columns per character). It's
made from 8 LED modules wahc 7 rows by 20 columns.
Electriclaly, it's wired as a 28*40 matrix. This needs a total of 68
drives (28 of one flavour, 40 of the other).any other electrical
arrangement (7*160, 14*80 or 56*20) needs more driver stages.
There were a few early calculators that did static registers with per-
digit decoders and drivers, but they quickly went to multiplexing, in
the days of discrete and SSI, long before LSI and pin-count issues.
And, of course, the multiplexing fit naturally with serial architecture.
I think most caclautors calcuated on digit at a time, so there was a
natural way to shift along the digits as part of the arithmetic
operation. Adding a multiplexed display to that was quire simple.
Converserly, many of the cheap LED digital clocks used a 4-digit
non-multiplexed dispaly .With these, multiplexing the outputs of the
counters did mean extra logic, and you had enough pins on a 40 pin
package to directly drive all the display segments. And since such clocks
were mains-powered (the timing reference came from the mains too), there
was little incentive to save power.
-tony